$\begin{cases}a(1)=20\\\\ a(n)=a(n-1)-17 \end{cases}$ Find the $3^{\text{rd}}$ term in the sequence.
Solution: This is a recursive formula. It tells us that the first term is $20$ and that the common difference is $-17$. $\begin{aligned} {a(1)}&=20 \\\\ {a(2)}&={a(1)}-17=3 \\\\ {a(3)}&={a(2)}-17=-14 \end{aligned}$ The $3^\text{rd}$ term is $-14$.